On normality of some elliptic functional differential operators (Q1272013)

The author obtains necessary and sufficient conditions for normality of the elliptic functional differential operators defined by \(A=A_0+A_1\), where \(A_0v= \Delta v\), \(v\in D(A_0)\) \[ D(A_0)= \bigl\{v\in W^2_2 (Q):Bv= 0\bigr\}, \] \(Bv=v |_{\partial \Omega}\) or \(Bv= {\partial v\over \partial\nu} |_{\partial Q}\); \(A_1v(x)= av(g(x)), a\neq 0\), \(a\in\mathbb R\) and \(g\) is a transformation of class \(C^3\) mapping a bounded domain \(V\subset \mathbb R^n\) onto \(g(V)\) such that \(| J_g(x) |\neq 0\) and \(g(Q)\subset Q\), \(Q\) being a bounded domain in \(\mathbb R^n\).